We study the thermodynamic properties of the Hopfield model of an autoassociative memory. If N denotes the number of neurons and M(N) the number of stored patterns, we prove the following results: If M ⁄N ↓ 0 as N ↑ ∞, then there exists an infinite number of infinite volume Gibbs measures for all temperatures T < 1 concentrated on spin configurations that have overlap with exactly one specific pattern. Moreover, the measures induced on the overlap parameters are Dirac measures concentrated on a single point. If M ⁄N → α, as N ↑ ∞ for a small enough, we show that for temperatures T smaller than some T(α) < 1, the induced measures can have support only on a disjoint union of balls around the previous points, but we cannot construct the infinite volume measures through convergent sequences of measures.